A109607 Sum of coprimes of n greater than 1.

0, 0, 0, 2, 3, 9, 5, 20, 15, 26, 19, 54, 23, 77, 41, 59, 63, 135, 53, 170, 79, 125, 109, 252, 95, 249, 155, 242, 167, 405, 119, 464, 255, 329, 271, 419, 215, 665, 341, 467, 319, 819, 251, 902, 439, 539, 505, 1080, 383, 1028, 499, 815, 623, 1377, 485, 1099, 671, 1025

Offset: 0

Author

Andrew Weimholt, Jul 31 2005

Keywords

• nonn
• look

Examples

			a(9) = 26 because 2,4,5,7,8 are coprime to 9 and 2+4+5+7+8 = 26.
		

Links

• Robert P. P. McKone, Table of n, a(n) for n = 0..14143

Crossrefs

Cf. A023896.

Programs

Mathematica

a[n_] := Total@Select[Range[2, n], CoprimeQ[n, #] &]; Table[a[n], {n, 0, 57}] (* Robert P. P. McKone, Nov 12 2023 *)

PARI

a(n) = sum(i=2, n-1, i*(gcd(i, n)==1)); \\ Michel Marcus, Mar 08 2013

PARI

a(n)=if(n<3,0,n*eulerphi(n)/2-1) \\ Charles R Greathouse IV, Mar 08 2013

Formula

a(n) = A023896(n) - 1. - Joerg Arndt, Mar 08 2013

G.f.: -x/(1 - x) + Sum_{k>=1} mu(k)*k*x^k/(1 - x^k)^3. - Ilya Gutkovskiy, May 28 2019

Extensions

Added "greater than 1" to name to match terms, Joerg Arndt, Mar 08 2013